Molecular Dynamics Using the Classical Drude Oscillator

Molecular Dynamics Using the Classical Drude Oscillator 

When the Drude particles are treated adiabatically, a SCF method must be used to solve for the displacements of the Drude particle, d, similarly to the dipoles Jtj in the induced dipole model. The implementation of the SCF condition corresponding to the Born-Oppenheimer approximation is straightforward and the real forces acting on the nuclei must be determined after the Drude particles have attained the energy minimum for a particular nuclear configuration. In the case of N polarizable atoms with positions r, the relaxed Drude particle positions r + d5CF are found by solving 

These equations define the force equilibria on the Drude particles 

This equation is the equivalent of Eq. (9-12) for the induced dipole model but has one important difference. Equation (9-13), the derivative of Eq. (9-12), is linear and standard matrix methods can be used to solve for the p. because Eq. (9-12) is a quadratic function of p , while Eq. (9-54) is not a quadratic function of d and thus matrix methods are usually not used to find the Drude particle displacements that minimize the energy. 

An important alternative to SCF is to extend the Lagrangian of the system to consider dipoles as additional dynamical degrees of freedom as discussed above for the induced dipole model. In the Drude model the additional degrees of freedom are the positions of the moving Drude particles. All Drude particles are assigned a small mass mo,i, taken from the atomic masses, m, of their parent atoms and both the motions of atoms and Drude particles (at positions r, and rdj = r, + d, ) are propagated 

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